|Date: Friday, December 01, 2017
Location: 3866 East Hall (4:15 PM to 5:15 PM)
Title: Symmetry and self-similarity in Riemannian geometry
Abstract: In 1893, Hurwitz showed that a Riemann surface of genus g >1 admits at most 84(g-1) automorphisms; equivalently, any 2-dimensional hyperbolic orbifold X has Area(X) >= pi / 42. In contrast, such a lower bound on volume fails for the n-dimensional torus T^n, which is closely related to the fact that T^m covers itself nontrivially. Which geometries admit bounds as above? Which manifolds cover themselves? In the last decade, more than 100 years after Hurwitz, powerful tools have been developed from the simultaneous study of symmetries of all covers of a given manifold, tying together Lie groups, their lattices, and their appearances in differential geometry. In this talk I will explain some of these recent ideas and how they lead to progress on the above (and other) questions.
Speaker: Wouter van Limbeek
Institution: U Michigan
Event Organizer: spatzier